Employment, Productivity and the Business Cycle

Fourth post in a series. Posts one, two and three.

Empirically-oriented macroeconomists have recognized since the early 20th century that output, employment and productivity move together over the business cycle. The fact that productivity falls during recessions means that employment varies less over the cycle than output does. This behavior is quite stable over time, giving rise to Okun’s law. In the US, Okun’s law says that the unemployment rate will rise by one point in each 2.5 point shortfall of GDP growth over trend — a ratio that doesn’t seem to have declined much since Arthur Okun first described it in the mid-1960s. [1]

It’s not obvious that potential should show this procyclical behavior. As I noted in the previous post, a naive prediction from a production function framework would be that a negative demand shock should reduce employment more than output, since business can lay off workers immediately but can’t reduce their capital stock right away. In other words, productivity should rise in recessions, since the labor of each still-employed worker is being combined with more capital.

There are various explanations for why labor productivity behaves procyclically instead. The most common focus on the transition costs of changing employment. Since hiring and firing is costly for businesses, they don’t adjust their laborforce to every change in demand. So when sales fall in recessions, they will keep extra workers on payroll — paying them now is cheaper than hiring them back later. Similarly, when sales rise businesses will initially try to get more work out of their existing employees. This shows up as rising labor productivity, and as the repeated phenomenon of “jobless recoveries.”

Understood in these terms, the positive relationship between output, employment and productivity should be a strictly short-term phenomenon. If a change in demand (or in other constraints on output) is sustained, we’d expect labor to fully adjust to the new level of production sooner or later. So over horizons of more than a year or two, we’d expect output and employment to change in proportion. If there are other limits on production (such as non-produced inputs like land) we’d expect output and labor productivity to move inversely, with faster productivity growth associated with slower employment growth or vice versa. (This is the logic of “robots taking the jobs.”) A short-term positive, medium term negative, long-term flat or negative relationship between employment growth and productivity growth is one of the main predictions that comes out of a production function. But it doesn’t require one. You can get there lots of other ways too.

And in fact, it is what we see.

prod-emp correl

The figure shows the simple correlation of employment growth and productivity growth over various periods, from one quarter out to 50 quarters. (This is based on postwar US data.) As you can see, over periods of a year or less, the correlation is (weakly) positive. Six-month periods in which employment growth was unusually weak are somewhat more likely to have seen weak productivity growth as well. This is the cyclical effect presumably due to transition costs — employers don’t always hire or fire in response to short-run changes in demand, allowing productivity to vary instead. But if sales remain high or low for an extended period, employers will eventually bring their laborforce into line, eliminating this relationship. And over longer periods, autonomous variation in productivity and labor supply are more important. Both of these tend to produce a negative relationship between employment and productivity. And that’s exactly what we see — a ten-year period in which productivity grew unusually quickly is likely to be one in which employment grew slowly. (Admittedly postwar US data doesn’t give you that many ten-year periods to look at.)

Another way of doing this is to plot an “Okun coefficient” for each horizon. Here we are looking at the relationship between changes in employment and output. Okun’s law is usually expressed in terms of the relatiojship between unemployment and output, but here we will look at it in terms of employment instead. We write

(1)    %ΔE = a (g – c)

where %ΔE is the percentage change in employment, g is the percentage growth in GDP, is a constant (the long-run average rate of productivity growth) and a is the Okun coefficient. The value of a says how much additional growth in employment we’d expect from a one percentage-point increase in GDP growth over the given period. When the equation is estimated in terms of unemployment and the period is one, year, a is generally on the order of 0.4 or so, meaning that to reduce unemployment by one point over a year normally requires GDP growth around 2.5 points above trend. We’d expect the coefficient for employment to be greater, but over short periods at least it should still be less than one.

Here is what we see if the estimate the equation for changes in output and employment for various periods, again ranging from one quarter up to ten years. (Again, postwar US data. The circles are the point estimates of the coefficients; the dotted lines are two standard errors above and below, corresponding to a standard 95% confidence interval.)

emp on output

What’s this show? If we estimate Equation (1) looking at changes over one quarter, we find that one percentage point of additional GDP growth is associated with just half a point of additional employment growth. But if we estimate the same equation looking at changes over two years, we find that one point of additional GDP growth is associated with 0.75 points of additional employment growth.

The fact that the coefficient is smallest for the shorter periods is, again, consistent witht he conventional understanding of Okun’s law. Because hiring and firing is costly, employers don’t fully adjust staffing unless a change in sales is sustained for a while. If you were thinking in terms of a production function, the peak around 2 years represents a “medium-term” position where labor has adjusted to a change in demand but the capital stock has not.

While it’s not really relevant for current purposes, it’s interesting that at every horizon the coefficient is significantly below zero. What this tells us is that there is no actual time interval corresponding to the “long run” of the model– a period long enough for labor and the capital stock to be fully adjusted but short enough that technology is fixed. Over this hypothetical long run, the coefficient would be one. One way to think about the fact that the estimated coefficients are always smaller, is that any period long enough for labor to adjust, is already long enough to see noticeable autonomous changes in productivity. [2]

But what we’re interested in right now is not this normal pattern. We’re interested in how dramatically the post-2008 period has departed from it. The past eight years have seen close to the slowest employment growth of the postwar period and close to the slowest productivity growth. It is normal for employment and productivity to move together for a couple quarters or a year, but very unusual for this joint movement to be sustained over nearly a decade. In the postwar US, at least, periods of slow employment growth are much more often periods of rapid productivity growth, and conversely. Here’s a regression similar to the Okun one, but this time relating productivity growth to employment growth, and using only data through 2008.

prod on empWhile the significance lines can’t be taken literally given that these are overlapping periods, the figure makes clear that between 1947 and 2008, there were very few sustained periods in which both employment and productivity growth made large departures from trend in the same direction.

Put it another way: The past decade has seen exceptionally slow growth in employment — about 5 percent over the full period. If you looked at the US postwar data, you would predict with a fair degree of confidence that a period of such slow employment growth would see above-average productivity growth. But in fact, the past decade has also seen very low productivity growth. The relation between the two variables has been much closer to what we would predict by extrapolating their relationships over periods of a year. In that sense, the current slowdown resembles an extended recession more than it does previous periods of slower growth.

As I suggested in an earlier post, I think this is a bigger analytic problem than it might seem at first glance.

In the conventional story, productivity is supposed to be driven by technology, so a slowdown in productivity growth reflects a decline in innovation and so on. Employment is driven by demographics, so slower employment growth reflects aging and small families. Both of these developments are negative shifts in aggregate supply. So they should be inflationary — if the economy’s productive potential declines then the same growth in demand will instead lead to higher prices. To maintain stable prices in the face of these two negative supply shocks, a central bank would have to raise interest rates in order to reduce aggregate spending to the new, lower level of potential output. Is this what we have seen? No, of course not. We have seen declining inflation even as interest rates are at historically low levels. So even if you explain slower productivity growth by technology and explain slower employment growth by demographics, you still need to postulate some large additional negative shift in demand. This is DeLong and Summers’ “elementary signal identification point.”

Given that we are postulating a large, sustained fall in demand in any case, it would be more parsimonious if the demand shortfall also explained the slowdown in employment and productivity growth. I think there are good reasons to believe this is the case. Those will be the subject of the remaining posts in this series.

In the meantime, let’s pull together the historical evidence on output, employment and productivity growth in one last figure. Here, the horizontal axis is the ten-year percentage change in employment, while the vertical axis is the ten-year percentage change in productivity. The years are final year of the comparison. (In order to include the most recent data, we are comparing first quarters to first quarters.) The color of the text shows average inflation over the ten year period, with yellow highest and blue lowest. The diagonal line corresponds to the average real growth rate of GDP over the full period.

e-p scatter

What we’re looking at here is the percentage change in productivity, employment and prices over every ten-year period from 1947-1957 through 2006-2016. So for instance, growth between 1990 and 2000 is represented by the point labeled “2000.” During this decade, total employment rose by about 20 percent while productivity rose by a total of 15 percent, implying an annual real growth of 3.3 percent, very close to the long-run average.

One natural way to think about this is that yellow points below and to the right of the line suggest negative supply shocks: If the productive capacity of the economy declines for some reason, output growth will slow, and prices will rise as private actors — abetted by a slow-to-react central bank — attempt to increase spending at the usual rate. Similarly, blue points above the line suggest positive supply shocks. Yellow points above the line suggest positive demand shocks — an increase in spending can increase output growth above trend, at least for a while, but will pull up prices as well. And blue points below the line suggest negative demand shocks. This, again, is Delong and Summers’ “elementary signal identification point.”

We immediately see what an outlier the recent period is. Both employment and productivity growth over the past ten years have been drastically slower than over the preceding decade — about 5 percent each, down from about 20 percent. 2000-2010 and 2001-2011 were the only ten-year periods in postwar US history when total employment actually declined. The abruptness of the deceleration on both dimensions is a challenge for views that slower growth is the result of deep structural forces. And the combination of the slowdown in output growth with falling prices — especially given ultra-low interest rats — strongly suggests that we’ve seen a negative shift in desired spending (demand) rather than in the economy’s productive capacities (supply).

Another way of looking at this is as three different regimes. In the middle is what we might call “the main sequence” — here there is steady growth in demand, met by varying mixes of employment and productivity growth. On the upper right is what gets called a “high-pressure economy,” in which low unemployment and strong demand draw more people into employment and facilitates the reallocation of labor and other resources toward more productive activity, but put upward pressure on prices. On the lower left is stagnation, where weak demand discourages participation in the labor force and reduces productivity growth by holding back investment, new business formation and by leaving a larger number of those with jobs underemployed, and persistent slack leads to downward pressure on prices (though so far not outright deflation). In other words, macroeconomically speaking the past decade has been a sort of anti-1960s.


[1] There are actually two versions of Okun’s law, one relating the change in the unemployment rate to GDP growth and one relating the level of unemployment to the deviation of GDP from potential. The two forms will be equivalent if potential grows at a constant rate.

[2] The assumption that variables can be partitioned into “fast” and “slow” ones, so that we can calculate equilibrium values of the former with the latter treated as exogenous, is a very widespread feature of economic modeling, heterodox as much as mainstream. I think it needs to be looked at more critically. One alternative is dynamic models where we focus on the system’s evolution over time rather than equilibrium conditions. This is, I suppose, the kind of “theory” implied by VAR-type forecasting models, but it’s rare to see it developed explicitly. There are people who talk about a system dynamics approach, which seems promising, but I don’t know much about them.

6 thoughts on “Employment, Productivity and the Business Cycle”

  1. Ukkk! This really is wonkish!

    “[…] yellow points below and to the right of the line suggest […]”
    But all yellow points are below to the left. I don’t completely understand this picture.

    Speaking of employment growth, I think we should differentiate between increase in population and increase in the partecipation rate. For example, suppose that in both the countries A and B there are 100 people, 50% of whom are working. In country A, after 10 years, the population is the same, but the partecipation rate increases to 55%; in country B, population increases to 110 but partecipation rate stays the same. In both cases employment grows from 50 to 55, but we see a very different macroeconomic evolution in term of market power, consumption etc..
    There is a problem doing this comparison because partecipation rate depends also on social and perhaps technical limits when we take in account the share of population that is not supposed to work in general or is “producing” in a non-market sense, for example in some societies women are not supposed to work outside the household, in other societies the age bracket during wich one is supposed to work might be different etc.. However, if we are speaking of the effects of demand on productivity, I think that an increase in employment in relative terms (increased partecipation rate) is very different from an absolute increase of population.

    Speaking of the “production function”, I think that the usual way of comparing aggregate “real” capital (meaning, capital as a lump of “real” value) to the number of workers is meaningless, and it would be better to assume that capital is directly proportional to workers, through a proportion that depends on “technology”.
    Let’s take as an example a delivery company, that uses trucks as capital and drivers as workers. It is obvious that the number of drivers per truck is somewhat fixed, though there might be some elasticity in the short run. This elasticity means that there might be periods in which drivers are overworked, and periods where some workers are idle.
    Suppose that the optimal proportion is 1.5 drivers per truck, and the company owns 10 trucks and employs 15 drivers.
    In a period of slack of demand, the company only uses 8 of the trucks, and rotates the drivers in such a way that 15 drivers do the work that 12 would do in other situations. The company doesn’t fire the remaining 3 drivers for the reason you outlined in the post, and this causes the short term slack in productivity.
    On a longer timeframe, the company might fire the 3 excess drivers, or simply not employ new drivers when the old ones retire. At this point the company has 12 drivers and 10 trucks, so in some sense it is overcapitalised, but 2 of the 10 trucks are not used so in reality the “capital per worker” did not increase.
    In a period of high demand, the company can overwork both the drivers and the trucks, but sooner or later will have to buy a new truck and hire some additional drivers, more or less in proportion.
    As times goes by, the company will have to scrap old trucks and buy new ones. But as technology progresses, the new trucks will be better than the old ones, and thus will have an higher “real” value than the old ones, so the “real capital per worker” increases; but this increase in capital per worker is not a form of “accumulation” of capital, just a consequence of replacing obsolete capital with technologically advanced capital.
    I say this because some time ago I was interested in the “Goodwin cycle” and so I found the original Goodwin article on the web. I was very disappointed because it treated “capital accumulation” as if it was a continuous accumulation of stuff, in such a way that doesn’t really make sense, and the increase in population as some sort of neomalthusian thing. (I still think that the Goodwin cycle makes a lot of sense but it should be defined in an entirely different way).

    So, starting from my definition of the “production function”, I have big problems with the idea that a persistent slowdown in productivity, while employment is growing (so new capital goods are added to the market) can be blamed on “demand” factors, because those demand factors should also keep employment low in absolute terms. On the other hand there is a coincidence of this slowdown with a very big demand crisis, so it is quite obvous that the two are related.

    I propose the following (contradictory) hypotheses:
    1) we suck at calculating “real” growth, productivity did really rise, but because of low inflation we don’t see it because new, better goods are priced just above old goods;
    2) there is a slowdown in the rate of substitution of capital goods, that keeps down technological progress;
    3) the “real” value of goods depends very much on the market, but some goods are locally produced, other for the international market, some goods are luxury goods for the rich, other basic goods for everyone etc. A big crisis might have different effects on some markets than on others, so that for example the price of goods for the inner market might be more affected than the price for export goods, that depends on demand outside the USA; we are not really good at calculating “real” values and so this price effect crawls into the calculation of productivity (this might happen together with 1).

    1. Ukkk! This really is wonkish!

      Yes, I’m sorry. What you’re reading now is really notes from work in progress rather than finished products for public consumption.

      all yellow points are below to the left.

      Right, this is important information. In the postwar US, the periods of highest inflation saw average employment growth and very low productivity growth, so slower output growth overall. This suggests that the high inflation is explained by a negative shift in supply rather than a more rapid growth in demand. Note there are some yellow-green points on the right, representing periods running from the late 1960s through the early 1970s. These are ore consistent with inflation due to excessive demand growth.

      I think we should differentiate between increase in population and increase in the partecipation rate.

      That’s reasonable. I could redo this on a per-capita basis, maybe I will. On the other hand, population is at least somewhat endogenous to demand/labor-market conditions, at least in a country with large gross migration flows.

      On your trucks example, you’re right and I think this is a critical point. Technological progress is not just “out there,” it is embodied in concrete means of production and organizations. So it is natural to expect that more rapid output growth will be associated with more rapid technological change.

      On your second point, I share your concern that long-term comparisons of output and output growth may be meaningless because the measurement of “real” output involves a number of assumptions which are not only uncertain and arbitrary but don’t have single correct values even in principle. The thought has crossed my mind that perhaps one reason “real” growth rates are so stable is that the entities that produce the price adjustments end up (through their sociology, not as a conscious choice) adjusting the growth of the price level to whatever level is needed for that.

      But for now — maybe wrongly — I am going to proceed as if “real” output is a material fact.

  2. I really like this framing. It’s very tidy. But it also risks overgeneralising far too much — as is often the case with frameworks that purport to deal with very Big Questions while remaining compact and tidy. For example, this is not at all correct, I think:

    “One natural way to think about this is that yellow points below and to the right of the line suggest negative supply shocks: If the productive capacity of the economy declines for some reason, output growth will slow, and prices will rise as private actors — abetted by a slow-to-react central bank — attempt to increase spending at the usual rate.”

    This assumes that all inflation is demand pull. In fact none of your sample contains demand pull inflation because of the way you have cut it. We saw demand pull inflation in the Korean War (1950-51) and in the Vietnam War (1968-70) but these were brief. Indeed, theoretically we should expect true demand pull inflation to always be brief. Because these periods your ten year rolling average will not pick them up.

    Instead what you are picking up is sustained inflation. And we know that sustained inflations are almost always cost push. These are the inflations that you are picking up below the line — they run through the the oil price shock-cum-wage inflation.

    So why do the high-price, high employment, low productivity sectors fall neatly where a simplified AS-AD model would assume even though an extensive investigation of these inflations would show them not to be cost push? Simple. You are mainly dealing with an identity here — and productivity is the variable that ‘gives’… because it is calculated as a residual.

    Yes, you have directly measured high prices. Yes, you have directly measured high employment growth. But output growth is low so you get low productivity as a residual. The real question is not why productivity growth is slow in these periods but why output growth is slow.

    So, why is output growth slow in the 1970s stagnation period? Because the supply-side has fallen off in the sense of oil price declines. This, however, has little to do with demand pull inflation. It has to do with price hikes in commodities markets. If you’re not careful about how you interpret this you’ll end up falling into the anti-Keynesian camp of the 1970s — that is, you’ll end up a monetarist, which is precisely what Delong and Summers are.

    1. “So why do the high-price, high employment, low productivity sectors fall neatly where a simplified AS-AD model would assume even though an extensive investigation of these inflations would show them not to be cost push?”

      Should read:

      “So why do the high-price, high employment, low productivity sectors fall neatly where a simplified AS-AD model would assume even though an extensive investigation of these inflations would show them to be cost push?”

    2. I really like this framing. It’s very tidy. But it also risks overgeneralising far too much

      Yes, very true. If we are looking at 10-year periods over a total of 70 years, that’s the equivalent of only a dozen or so datapoints. It will be pretty easy to do the same exercise for other OECD countries though. Hopefully I’ll get to that fairly soon and then we’ll have a better sense of how useful this frame is.

      This assumes that all inflation is demand pull.

      No, my intention was just the opposite. Obviously the post was not very clear! Demand pull inflation should show up as a combination of higher output *and* higher inflation, since “potential output” is not a sharp line. And probably the higher output will be reflected more in employment than productivity. Conversely, weak demand will show lower inflation, slower output growth and probably much slower employment growth. By that heuristic, the period of high inflation in the late 1970s-early 1980s looks very clearly like a supply-side rather than a demand-side phenomenon. (The earlier period of rising inflation in the late 1960s-early 1970s is more plausibly an effect of strong demand.)

      You are right that productivity is measured as a residual. But I don’t think it’s a residual substantively, or at least not entirely one. I mean, you don’t think changes in output and employment are strictly independent, do you?

      1. You’re right. You said negative supply shock. But most will use this framework to argue negative demand shock. I’d be careful with that. The framework tends to push you toward that interpretation.

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